Devices and methods of flow measurements are disclosed in U.S. Ser. Nos. 09/073,061, 09/117,416, all assigned to Radi Medical Systems AB, Sweden.
In particular Ser. No. 09/073,061 relates to a method of flow measurements by thermo-dilution, wherein the time measurements are triggered by a pressure pulse detected as a result of the injection of a bolus dose of saline. The general theory described therein fully applies to the present invention, and therefore the entire disclosure thereof is incorporated herein.
Nevertheless, the discussion therein is repeated below for ease of understanding.
Application of the thermodilution principle in the coronary sinus was introduced by Ganz (Ganz et al, xe2x80x9dMeasurement of coronary sinus blood flow by continuous thermodilution in man, Circulation 44:181-195, 1971). A small catheter is introduced deeply into the coronary sinus and cold saline is delivered at its tip. Theoretically, flow can be calculated from the changes in blood temperature, registered by a thermistor close to the outlet of the coronary sinus. An advantage of this method is that only right heart catheterization is required.
The principle of thermo-dilution involves injecting a known amount of cooled liquid, e.g. physiological saline in a blood vessel. After injection the temperature is continuously recorded with a temperature sensor attached to the tip of a guide wire that is inserted in the vessel. A temperature change due to the cold liquid passing the measurement site, i.e. the location of the sensor, will be a function of the flow.
There are various methods of evaluating the temperature signal for diagnostic purposes. Either one may attempt to calculate the volume flow, or one may use a relative measure, where the flow in a xe2x80x9crest conditionxe2x80x9d is compared with a xe2x80x9cwork conditionxe2x80x9d, induced by medicaments.
The latter is the simpler way, and may be carried out by measuring the width at half height of the temperature change profile in the two situations indicated, and forming a ratio between these quantities.
Another way of obtaining a ratio would be to measure the transit time from injection and until the cold liquid passes the sensor, in rest condition and in work condition respectively.
The former method, i.e. the utilization of the volume flow parameter as such, requires integration of the temperature profile over time in accordance with the equations given below                                           (            1            )                    ⁢                      xe2x80x83                    ⁢                      Q                          r              ⁢                              xe2x80x83                            ⁢              e              ⁢                              xe2x80x83                            ⁢              s              ⁢                              xe2x80x83                            ⁢              t                                      ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                              V            /                                                            ∫                                      t                    1                                                                    t                  0                                            ⁢                                                (                                                            T                                              r                        ,                                                  xe2x80x83                                                ⁢                        m                                                              /                                          xe2x80x83                                        ⁢                                          T                                              r                        ,                                                  xe2x80x83                                                ⁢                        l                                                                              )                                ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                              ⁢                      xe2x80x83                    ∝                      xe2x80x83                    ⁢                      V            /                                                            ∫                                      t                    1                                                                    t                  0                                            ⁢                                                (                                                            T                                              r                        ,                                                  xe2x80x83                                                ⁢                        0                                                              ⁢                                          xe2x80x83                                        -                                          xe2x80x83                                        ⁢                                          T                                              r                        ,                                                  xe2x80x83                                                ⁢                        m                                                                              )                                ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                                                        (        3.1        )                                                      (            2            )                    ⁢                      xe2x80x83                    ⁢                      Q                          w              ⁢                              xe2x80x83                            ⁢              o              ⁢                              xe2x80x83                            ⁢              r              ⁢                              xe2x80x83                            ⁢              k                                      ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                              V            /                                                            ∫                                      t                    1                                                                    t                  0                                            ⁢                                                (                                                            T                                              w                        ,                                                  xe2x80x83                                                ⁢                        m                                                              /                                          xe2x80x83                                        ⁢                                          T                                              w                        ,                                                  xe2x80x83                                                ⁢                        l                                                                              )                                ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                              ⁢                      xe2x80x83                    ∝                      xe2x80x83                    ⁢                      V            /                                                            ∫                                      t                    1                                                                    t                  0                                            ⁢                                                (                                                            T                                              w                        ,                                                  xe2x80x83                                                ⁢                        0                                                              ⁢                                          xe2x80x83                                        -                                          xe2x80x83                                        ⁢                                          T                                              w                        ,                                                  xe2x80x83                                                ⁢                        m                                                                              )                                ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                                                        (        3.2        )            
wherein
V is the volume of injected liquid
Tr,m is the measured temperature at rest condition
Tr,1 is the temperature of injected liquid at rest condition
T0 is the temperature of the blood, i.e. 37xc2x0 C.
Tw,m is the measured temperature at work condition
Tw,1 is the temperature of injected liquid at work condition
Q is the volume flow
These quantities may then be used directly for assessment of the condition of the coronary vessels and the myocardium of the patient, or they may be ratioed as previously discussed to obtain a CFR, i.e. CFR=Qwork/Qrest.
The latter method, i.e. determination of the transit time requires an accurate time measurement, in view of the relatively small distances in question, about 10 cm or less from injection to measurement site.
To obtain a correct measurement, the time has to be measured with some accuracy. Using a simple stop watch, which is a common means of timing, is far too inaccurate for obtaining reliable transit times.
The flow F may be obtained as follows, which is a derivation for a similar technique, namely the indicator dilution technique. This is based on a rapidly injected amount of some kind of indicator, the concentration of which is measured.
Suppose that the flow through a branching vascular bed is constant and equals F, and that a certain well-known amount M of indicator is injected into this bed at site A (see FIG. 7). After some time, the first particles of indicator will arrive at the measuring site B. The concentration of indicator at B, called c(t), will increase for some time, reach a peak and decrease again. The graphic representation of indicator concentration as a function of time is called the indicator dilution curve.
Consider M as a large number of indicator particles (or molecules). The number of particles passing at B during the time interval xcex94t, between ti and ti+1, equals the number of particles per unit time multiplied by the length of the time interval, in other words: c(ti)xc2x7Fxc2x7xcex94t (FIG. 8).
Because all particles pass at B between t=0 and t=∞, this means that:                               M          =                                    lim                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                ⁢                                  xe2x80x83                                →                                  xe2x80x83                                ⁢                0                                      ⁢                                          ∑                                  i                  ⁢                                      xe2x80x83                                    =                                      xe2x80x83                                    ⁢                  0                                ∞                            ⁢                                                (                                                                                    c                        ⁡                                                  (                                                      t                            i                                                    )                                                                    ·                      F                      ·                      Δ                                        ⁢                                          xe2x80x83                                        ⁢                    t                                    )                                ⁢                                  xe2x80x83                                ⁢                or                                                    ⁢                  
                ⁢                  M          =                                                    ∫                ∞                            0                        ⁢                                                            c                  ⁡                                      (                    t                    )                                                  ·                F                ·                                  ⅆ                  t                                            ⁢                              xe2x80x83                            ⁢              or                                      ⁢                  
                ⁢                  F          ⁢                      xe2x80x83                    =                      xe2x80x83                    ⁢                      M                                                            ∫                  ∞                                0                            ⁢                                                                    xe2x80x83                                    ⁢                                      c                    ⁡                                          (                      t                      )                                                                      ·                                  ⅆ                  t                                                                                        (        3.3        )            
and it is the last expression which is used in most methods to calculate systemic flow as outlined above. Essential features of this approach is that the amount M of injected indicator should be known whereas no knowledge about the volume of the vascular compartment is needed.
The calculation of volume is more complex. For this purpose, the function h(t) is introduced which is the fraction of indicator, passing per unit of time at a measurement site at time t. In other words, h(t) is the distribution function of transit times of the indicator particles. If it is assumed that the flow of the indicator is representative for flow of the total fluid (complete mixing), h(t) is also the distribution function of transit times of all fluid particles. Suppose the total volume of fluid is made up of a very large number of volume elements dVi which are defined in such a way that dVi contains all fluid particles present in the system at t=0, with transit times between ti and ti+1. The fraction of fluid particles requiring times between ti and ti+1 to pass the measurement site, is h(ti)xc2x7xcex94t by definition. Because the rate at which the fluid particles pass at the measurement site, equals F, the rate at which the particles making up dVi pass at the measurement site is Fxc2x7h(ti)xc2x7xcex94t. The total volume of dVi equals the time ti required for all particles segments in dVi to pass at the measurement site multiplied by the rate at which they leave. In other words:
dVi=tixc2x7Fxc2x7h(ti)xc2x7xcex94txe2x80x83xe2x80x83(3.4)
and by integration:                     V        =                  F          ⁢                                                    ∫                ∞                            0                        ⁢                                          t                ·                                  h                  ⁢                                      (                    t                    )                                                              ⁢                              ⅆ                t                                                                        (        3.5        )            
The integral in the equation above represents the mean transit time Tmn, which is the average time needed by one particle to travel from an injection site to a measurement site. Therefore:
V=Fxc2x7Tmnxe2x80x83xe2x80x83(3.6)
or:
F=V/Tmn; Tmn=V/Fxe2x80x83xe2x80x83(3.7)
which states the fundamental fact that flow equals volume divided by mean transit time.
The mean transit time (Tmn) can now be calculated easily from the indicator or thermo dilution curve in the following way. When looking at the hatched rectangle in FIG. 8, it can be seen that the number of indicator particles passing between ti and ti+1, equals the number of particles c(ti)xc2x7F passing per unit of time, multiplied by the length of the time interval, xcex94t, in other words: c(ti)xc2x7Fxc2x7xcex94t. Therefore, the total (summed) transit time of all these indicator particles together equals tixc2x7c(ti)xc2x7Fxc2x7xcex94t. The total transit time of all indicator particles together, by integration, is                                                         ∫              0                        ⁢                                          xe2x80x83                            ⁢                              t                ·                                              ∞                ⁢                  xe2x80x83                ⁢                              c            ⁡                          (              t              )                                ·          F          ·                      ⅆ            t                                              (        3.8        )            
and the mean transit time of the indicator particles can be obtained by dividing equation 3.8 by the total number of particles M, resulting in:                               T                      m            ⁢                          xe2x80x83                        ⁢            n                          =                                                                                                  ∫                    0                                    ⁢                                                            xe2x80x83                                        ⁢                                          t                      ·                                                                      ∞                            ⁢                              xe2x80x83                            ⁢                                                c                  ⁡                                      (                    t                    )                                                  ·                F                ·                                  ⅆ                  t                                                      M                    ⁢                      xe2x80x83                    ⁢          or                                    (        3.9        )                                          T                      m            ⁢                          xe2x80x83                        ⁢            n                          ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                              F            M                    ⁢                      xe2x80x83                    ⁢                                                    ∫                0                            ⁢                                                xe2x80x83                                ⁢                                  t                  ·                                                      ∞                    ⁢                      xe2x80x83                    ⁢                                    c              ⁡                              (                t                )                                      ·                          ⅆ              t                                                          (        3.10        )            
By substitution of equation 3.3 in 3.10, Tmn is obtained:                               T                      m            ⁢                          xe2x80x83                        ⁢            n                          ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                                                                              ∫                  0                                ⁢                                                      xe2x80x83                                    ⁢                                      t                    ·                                                              ∞                        ⁢                          xe2x80x83                        ⁢                                          c                ⁡                                  (                  t                  )                                            ·                              ⅆ                t                                                                                        ∫                ∞                            0                        ⁢                                                            xe2x80x83                                ⁢                                  c                  ⁡                                      (                    t                    )                                                              ·                              ⅆ                t                                                                        (        3.11        )            
Equation 3.11 describes how mean transit time Tmn can be calculated from the indicator dilution curve c(t). In the assessment of myocardial in which the contrast agent is used as the indicator, because the amount of injected contrast agent is unknown and changing (because of the necessary leakage of the contrast agent into the aorta and the unknown and changing distribution of contrast agent over the different branches of the coronary arterial tree), use of Tmn is advantageous because no knowledge about the amount of injected indicator is necessary.
Although the above derivation was made for the mentioned indicator dilution technique, the result is the same for thermo-dilution since the same distribution function may be employed, and the skilled man will easily adjust the equations accordingly.
The prior art pressure pulse triggering of the time measurements, although improving the method considerably, has some drawbacks. For example, the sensitivity in the pressure measurement may not be adequate due to the magnitude of the pulse being quite low; therefore, the accuracy may be negatively influenced.
Thus, there is a need for an improved triggering of the measurement.
The inventors have realized that a previous problem acknowledged in connection with thermo-dilution can be used to an advantage for triggering purposes. Namely, when a bolus cold saline is injected into a catheter where a wire carrying the sensor unit and electrical leads for signal transmission is located, the lead resistance will be instantly affected by the cold saline by a change in the resistivity. This is a problem, however, because the change must be countered in order to arrive at a correct output signal.
This compensation can be done, and is one of the issues discussed in our pending Swedish application 9901962-2, corresponding to U.S. provisional No. 60/136,401.
Thus, in accordance with the present invention, the resistivity change is recorded as a resistance variation curve. Various parts of the recorded curve, or the entire curve, can be mathematically processed to yield a starting point for the determination for a transit time of the injected liquid. In this way, the accuracy in the time measurement is significantly improved.
So long as detectable signals are obtained, the method of flow determination according to the invention is advantageous in that it is independent of: (a) the injected amount of bolus liquid and (b) the temperature of the injected liquid.